Question : Find the smallest number which when divided by 19 and 23 gives remainders of 13 and 17 respectively.
Option 1: 419
Option 2: 429
Option 3: 431
Option 4: 437
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Correct Answer: 431
Solution : The difference between divisor and remainder, i) 19 – 13 = 6 ii) 23 – 17 = 6 The difference between the divisor and remainder is the same. The LCM of 19 and 23 is 437. To get the smallest number, which gives the remainder of 13 and 17 when divided by 19 and 23, we have to subtract 5 from the LCM of 19 and 23. The smallest number = LCM – 6 = 437 – 6 = 431 Hence, the correct answer is 431.
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Question : What is the least number which, when divided by 60, 84, and 96, leaves remainders of 28, 52, and 64, respectively?
Option 1: 3318
Option 2: 3360
Option 3: 3392
Option 4: 3328
Question : Directions: In the following question, find the odd number from the given alternatives.
Option 1: 63
Option 2: 23
Option 3: 17
Option 4: 13
Question : Find the smallest natural number $x$ that must be subtracted from 1800 so that $(1800 - x)$, when divided by 7, 11 and 23, will leave 5 as the remainder in each case.
Option 1: 24
Option 2: 25
Option 3: 26
Option 4: 20
Question : Find the second smallest number which, when divided by 81 or 63, leaves a remainder of 7 in each case.
Option 1: 1246
Option 2: 1141
Option 3: 1362
Option 4: 1137
Question : What is the greatest number which, on dividing 342 and 480, leaves remainders of 6 and 4 respectively?
Option 1: 14
Option 2: 4
Option 3: 7
Option 4: 28
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